Determine the kinetic energy of the planar pendulum of Example 1.1.
Kinematics of a planar pendulum
Consider the planar pendulum shown in Figure 1.3, where the orthogonal unit vectors e1 and e2 are fixed to the pendulum and they share the motion of the pendulum. The unit vectors i, j, and k, which point along the X, Y and Z directions, respectively, are fixed in time. The velocity and acceleration of the planar pendulum P with respect to point O are the quantities of interest. The position vector from point O to point P is written as
Making use of Eqs. (1.2) and (1.8) and noting that both h and L are constant with respect to time and the angular velocity v , the pendulum velocity is
In arriving at Eqs. (b) and (c), the following relations have been used.
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